(i) Prove that current flowing through an ideal inductor connected across ac source, lags the voltage in phase by .
(ii) An inductor of self inductance 100 mH, and a bulb are connected in series with ac source of rms voltage 10V, 50 Hz. It is found that effective voltage of the circuit leads the current in phase by .Calculate the inductance of the inductor used and average power dissipated in the circuit, if a current of 1 A flows in the circuit.
A device ‘X’ is connected to an ac source V = The variation of voltage, current and power in one cycle is shown in the following graph :
(i) An ac source generating a voltage V = V₀ sin ωt is connected to a capacitor of capacitance C. Find the expression of the current I flowing through it.Plot a graph of V and I versus ωt to show that the current is π/2 ahead of the voltage.
(ii) A resistor of 200Ω and a capacitor of 15 µF are connected in series to a 220 V, 50 Hz ac source.Calculate the current in the circuit and the rms
voltage across the resistor and the capacitor. Why the algebraic sum of these voltages is more than the source voltage ?
A device X is connected across an ac source of voltage V = V₀ sin ωt. The current through X is given as I = I₀sin(ωt +π/2).
(a) Identify the device X and write the expression for its reactance.
(b) Draw graphs showing variation of voltage and current with time over one cycle of ac, for X.
(c) How does the reactance of the device X vary with frequency of the ac ? Show this variation graphically.
(d) Draw the phasor diagram for the device X.
(a) Draw graphs showing the variations of inductive reactance and capacitive reactance with frequency of the applied ac source.
(b) Draw the phasor diagram for a series RC circuit connected to an ac source.
(c) An alternating voltage of 220 V is applied across a device X, a current of 0.25 A flows, which lag behind the applied voltage in phase by π/2 radian.If the same voltage is applied across another device Y, the same current flows but now it is in phase with the applied voltage.
(i) Name the devices X and Y.
(ii) Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y.
An ac voltage V = V₀ sin ωt is applied to a pure inductor L. Obtain an expression for the current in the circuit. Prove that the average power supplied to an inductor over one complete cycle is zero.
In the following circuit, calculate (i) the capacitance of the capacitor, if the power factor of the circuit is unity, (ii) the Q-factor of this circuit. What is the significance of the Q-factor in ac circuit ? Given the angular frequency of the ac source to be 100rad/s. Calculate the average power dissipated in the circuit.